Trig Integrals...

It can be determined without the use of a calculator that the antiderivative of (sinx)^5 is -cosx + (2/3)(cosx)^3 - (1/5)(cosx)^5 + c. However, one calculator claims that the answer is -cosx + (2/3)(cosx)^3 - (1/5)(cosx)^5, whilst another claims the answer is [-(150cosx + 3cos5x - 25cos3x]/240. Show that, with the exception of the fact that the calculator displays do not show the constant, the three expressions are the same.

It can be determined without the use of a calculator that the antiderivative of (sinx)^5 is -cosx + (2/3)(cosx)^3 - (1/5)(cosx)^5 + c. However, one calculator claims that the answer is -cosx + (2/3)(cosx)^3 - (1/5)(cosx)^5, whilst another claims the answer is [-(150cosx + 3cos5x - 25cos3x]/240. Show that, with the exception of the fact that the calculator displays do not show the constant, the three expressions are the same.

You need to apply standard trig identities to -cosx + (2/3)(cosx)^3 - (1/5)(cosx)^5 and show that, within a constant, it is equal to [-(150cosx + 3cos5x - 25cos3x]/240.

If you need more help, please show all your work and say where you get stuck.